The paper "Regression Models and Life Tables" published by D.r. Cox in 1972 introduced an important new statistical methodology that has considerable application to cancer research. It provides a method for determining the effect of explanatory variables, such as patient characteristics, on survival. The object of this research is to develop supplementary statistical methodologies. In particular, methods will be developed to examine goodness of fit, measure strength of prediction, select variables from a large set, account for missing data, model random effects and perform small sample permutation tests. These methods have been developed for the usual "Least Squares Regression" and have been invaluable in nearly all areas of scientific research. The analogous methods for life table regression will put important new statistical tools in the hands of clinical researchers and biostatisticians. The necessary computer software will be developed so that the new methodologies can be used by other investigators. Related models used to test differences in survival curves and differences in patient history will be studied.